Modeling the visual detail of a moving gas can be a laborious task. The ability to control sampling can vary from method to method. Foster and Metaxas [1997] solve the Navier-Stokes equation in a uniformly voxelized grid and further propose a popular unconditionally stable model. De Witt et al. [2012] represent the velocity using the Laplacian eigenvectors as a basis for incompressible flow. The Navier-Stokes equation can also be solved in a Lagrangian frame of reference with Smoothed Particle Hydrodynamics (SPH) [Gingold and Monaghan 1977], or with a Vortex Method, obtained by taking the curl of the Navier-Stokes equation [Cottet and Koumoutsakos 2000]. Vortex Methods can store data on points [Park and Kim 2005], curves [Angelidis et al. 2006b; Weissmann and Pinkall 2010], or surfaces [Brochu et al. 2012], and can be solved with an integral, with a grid [Couet et al. 1981], or both [Zhang and Bridson 2014]. Some original approaches don't use the Navier-Stokes equation [Elcott et al. 2007], but use Kelvin's theorem. Chern et al. [2016] solve the Schrodinger equation in a grid.
To model different characteristics at different resolutions, multiple approaches can be combined and applied to a selective range of scales: Selle et al. [2005] advect vorticity carried by points and advect vorticity carried by sheets. Kim et al. [2008] advect procedurally generated detail. Pfaff et al. [2009] and Kim et al. [2012] show that the region of changing scale is located near boundaries, varying density and temperature.
In the methods that compute pressure explicitly, the boundary condition can be met as part of computing the pressure. For the boundary condition of Vortex Methods, a harmonic field may be needed, and the source and doublet panel method can be the method of choice. Panel methods are well researched in aerodynamics. An introduction of panel methods is provided by Erickson [1990]. Both the source and the doublet term may be required. Using only the source term may not prevent the flow from passing through cup-shaped colliders, as opposed to spheroid colliders for which the doublet contribution is very small. This may be the case of the single layer potential of Zhang and Bridson [2014]. Using only the doublet term may not account for colliders with changing volume, since the doublet term is not capable of generating or consuming volume. Park and Kim [2005] use vorticle panels, which also do not handle cup-shaped colliders. Also, vorticle panels may not generate or consume volume by themselves, and may induce a rotational field.
Therefore, there is a need for improved methods of computer graphic simulation of an incompressible gas.